Method and device for the determination of at least one parameter of a mixture of a support, water and gas

ABSTRACT

In order to measure at least one parameter of a mixture of carrier substance, water and gas, the permittivity value of the mixture is measured at different frequencies by means of a network analyzer ( 1 ) and a sensor. The measurements are entered into a mixing formula for forming a system of equations. From the system of equations, at least one parameter of the mixture can be determined. The method is also suited for the measurement of the location dependence of a parameter, e.g. for the measurement of the humidity distribution in concrete.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the priority of German patent application100 30 602.0, filed Jun. 21, 2000, the disclosure of which isincorporated herein by reference in its entirety.

BACKGROUND

[0002] The invention relates to a method and a device according to thepreamble of the independent claims where at least one parameter of amixture is to be determined, the components of which mixture comprise acarrier substance, water and gas.

[0003] A method of this type can in particular be used for determiningthe humidity state of concrete elements. The knowledge of the humiditystate of concrete elements is often indispensable for avoiding orassessing of damages, but also for carrying out building and renovationsteps. Furthermore, the humidity situation has to be known when layingfloors (tiles, parquets, etc) in lofts, when coating concrete surfaces,and when assessing the corrosion of rebars. Hence, the measurement ofhumidity is of particular importance in concrete construction as well.

[0004] Methods of this type can, however, also be used in other fields,such as in the characterisation of pharmaceuticals and food stuff, andwherever a parameter of a mixture of carrier substance, water and gashas to be determined, wherein the carrier substance can be solid orliquid.

[0005] In order to keep expense and costs small, a corresponding methodshould be non-destructive.

[0006] A method and a device for determining the humidity content ofporous building materials have been known from the patent DE 196 52 679C1. There, the humidity of the mixture is determined by feedingelectromagnetic waves of several frequencies to a sensor and bydetermining the frequency dependent permittivity value of the mixture bymeans of calibration data specifically provided for the sensor. By meansof a system of equations, based on the mixing formula of Polder-vanSanten/de Loor, which is solved for the frequency independentparameters, the volume fraction of the liquid water can be determined.

[0007] It has been found, however, that the accuracy of this method islimited.

SUMMARY OF THE INVENTION

[0008] Hence, it is a general object of the invention to provide amethod and a device of the type mentioned above that allow measurementsof a higher accuracy.

[0009] In a first aspect of the invention, the permittivity value of thebound water is entered into the mixing formula as a frequency dependentfunction. It has been found that a more realistic model of the system isachieved by this step and the measurement accuracy is improved.

[0010] In a second aspect of the invention, it is assumed that thecontribution of the bound water does not have to be taken into accountseparately. In this case, the following parameters (or values derivedfrom these parameters) are determined simultaneously from the system ofequations:

[0011] volume fraction v₁ of the gas,

[0012] volume fraction v₂ of the free water,

[0013] at least one of the depolarization factors N_(2j) of the freewater and

[0014] the conductivity of the free water.

[0015] With other words, these parameters are therefore all fitted tothe measured values, e.g. by calculus of observations, which provides abetter modelling of the system and therefore a higher accuracy ofmeasurement.

[0016] Any formula describing the permittivity value of the mixture independence of the permittivity value of the components and their volumefractions can be used as mixing formula, such as the equation ofPolder-van Santen/de Loor mentioned above. Preferably, however, a mixingformula described in the following is used.

[0017] A third aspect of the invention relates to the mixing formula.Preferably, a formula as follows is used$ɛ_{m} = {ɛ_{b} + {\sum\limits_{i = 1}^{n}\quad {\frac{v_{i}}{3} \cdot \left( {ɛ_{i} - ɛ_{b}} \right) \cdot {\sum\limits_{j = 1}^{3}\quad \frac{ɛ_{m}}{ɛ_{m} + {N_{ij} \cdot \left( {ɛ_{i} - ɛ_{m}} \right)}}}}}}$

[0018] with ε₁ and v₁ being the permittivity value and the volumefraction of the gas, ε₂ and v₂ the permittivity value and the volumefraction of the free water, ε₃ and v₃ the permittivity value and thevolume fraction of the bound water (if the same is to be taken accountof), ε_(b) the permittivity value of the carrier substance, and N_(1j),N_(2j) and N_(3j) the depolarization factors of an ellipsoidal cavity ofthe gas or the free water or the bound water, respectively, wherein n=3when taking the bound water into account and n=2 when neglecting thebound water.

[0019] If this mixing formula is measured at a sufficient number forfrequencies, a sufficiently determined or overdetermined system ofequations results, which allows to determine at least one of the unknownparameters, such as the volume fraction of the free water.

[0020] In a further aspect of the invention it is taken into accountthat the water fraction of the mixture, or another parameter to bedetermined, can vary as a function of the depth, i.e. the distance tothe surface of the mixture. In order to take this into account, severalmeasuring steps are carried out, in which the sensor is arranged at aknown distance from the mixture and is separated from the same by adielectric of known permittivity. In each measuring step the sensordetermines a value w_(k) depending on the integral permittivity valueε_(k) of the mixture in the measuring range. Then, an evaluation iscarried out, in which the depth dependence of the liquid water fractionis determined based on the different dependencies of the values w_(k)from the parameter to be determined.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Further embodiments, advantages and applications of the inventionresult from the dependent claims and from the now following descriptionwith reference to the figures, wherein:

[0022]FIG. 1 is a schematic set-up of a preferred embodiment of theinvention,

[0023]FIG. 2 is a sectional view of a surface sensor, and

[0024]FIG. 3 is a sectional view of a hollow wave guide sensor.

DETAILED DESCRIPTION OF THE INVENTION

[0025] The set-up of FIG. 1 comprises a permittivity value measuringapparatus 1 for a frequency dependent determination of the complexpermittivity value of a mixture. Further, it comprises a surface sensor2 for measuring solid mixtures, which can be placed against a smooth andflat surface, and a circular hollow waveguide sensor 3 for measuringliquid mixtures, which can be filled into sensor 3. The sensors 2 or 3are electrically connected in selectable manner to the permittivityvalue measuring device 1 via a coaxial transmission line 14. Thepermittivity value measuring device 1 comprises a vector networkanalyzer, which measures the real and imaginary part of the reflectionfactor of the used sensor. This reflection factor is converted to acomplex permittivity ε_(m) of the mixture by means of sensor specificcalibration data. Corresponding methods are known to the person skilledin the art.

[0026] For evaluating the measurements, a data processing system 4, suchas a conventional PC, is connected to the permittivity value measuringdevice 1 and controls the whole measuring and calculation process in themanner described in the following. A temperature sensor 5 serves todetect the temperature of the mixture to be examined.

[0027]FIG. 2 shows a sectional view through the surface sensor 2. It hasa rotationally symmetric design with an inner conductor 6 and an outerconductor 7, which are separated by a coaxial isolation layer 8,preferably of Teflon. On its measuring end, the temperature sensor 5 isarranged.

[0028] The surface sensor 2 can be placed against the smooth, flatsurface 9 of the mixture 10 to be measured, such that its measuringrange 11 extends into the mixture. As described further below, it canalso be arranged at a distance from the mixture 10 to be measured suchthat its measuring range 11 extends only partially into the mixture.

[0029] On a side facing the coaxial transmission line 14, the surfacesensor 2 has a tapered transition section 12. It guarantees a impedancematched connection of the surface sensor 2 to the coaxial line 14. Thetransition is formed by two cones with common tip. In such a geometry,the impedance and the cone angles are connected via the followingrelation: $\begin{matrix}{Z_{0} = {\frac{Z_{F0}}{2\pi \sqrt{ɛ_{C}}}\ln \frac{\tan \left( {\vartheta_{2}/2} \right)}{\tan \left( {\vartheta_{1}/2} \right)}}} & (1)\end{matrix}$

[0030] Herein, Z₀ is the impedance of the transition section (which isto be equal to the one of the coaxial cable and should e.g. be 50 Ohms),Z_(F0) the vacuum impedance (Z_(F0)={square root}{square root over(μ₀/ε₀)}=377 Ohm), ε_(c) the permittivity of the isolation layer 8, θ₁the angle of the inner cone of the inner conductor 6 and θ₂ the angle ofthe outer cone of the outer conductor 7.

[0031]FIG. 3 shows a sectional view of the hollow wave guide sensor 3.It again has a rotationally symmetric design with an inner conductor 6and an outer conductor 7, which are separated by a coaxial isolationlayer 8, preferably of Teflon. The outer conductor 7 extends beyond theisolation layer and the inner conductor and limits a cavity forreceiving the mixture 10 to be measured. Again, a transition section 12for an impedance matched connection with the coaxial transmission line14 can be provided.

[0032] Wit the sensors according to FIGS. 2 and 3 the permittivity isdetermined via the reflection of an electromagnetic wave. Thepermittivity can, however, also be measured in a transmissionmeasurement, where e.g. the damping and phase shift of anelectromagnetic wave upon transition through the mixture is measured. Inthat case the sensor consists of a sender and a receiver. Correspondingtechniques are known to the person skilled in the art.

[0033] The mixture to be measured can, as already mentioned, be in solidor liquid form. It comprises a carrier substance (preferably liquid orsolid concrete), which forms the predominant volume fraction of themixture, as well as water and gas, which are e.g. arranged in pores orcavities in the carrier substance.

[0034] For measuring at least one parameter of this mixture, we proceedas follows.

[0035] In a first step, the mixture 10 is brought into the measuringrange of the sensor 2 or 3, respectively. Then, its temperature T ismeasured by means of temperature sensor 5.

[0036] Now, the complex permittivity value ε_(m) of the mixture withinthe measuring range 11 is determined by means of the permittivity valuemeasuring device 1, namely at several measuring frequencies fi,preferably in a range between 10 kHz and 10 GHz, preferably 10 MHz and 1GHz.

[0037] These measurements are compared to a theoretical formula based ona model of the mixture, preferably: $\begin{matrix}{ɛ_{m} = {ɛ_{b} + {\sum\limits_{i = 1}^{n}\quad {\frac{v_{i}}{3} \cdot \left( {ɛ_{i} - ɛ_{b}} \right) \cdot {\sum\limits_{j = 1}^{3}\quad \frac{ɛ_{m}}{ɛ_{m} + {N_{ij} \cdot \left( {ɛ_{i} - ɛ_{m}} \right)}}}}}}} & (2)\end{matrix}$

[0038] Here, ε₁ and v₁ designate the permittivity value and volumefraction of the gas, ε₂ and v₂ the permittivity value and volumefraction of the free water, ε₃ and v₃ the permittivity value and volumefraction of the bound water, ε_(b) the permittivity value of the carriersubstance and N_(1j), N_(2j) and N_(3j) the depolarization factors of anellipsoidal cavity of the gas or the free water or the bound water,respectively. If the contributions of the bound water are taken intoaccount, n is equal to 3. If these contributions are neglected, n isequal to 2.

[0039] By entering the measured value ε_(m)(f_(i)) into equation (2) asystem of equations is obtained. If a sufficient number of measurementvalues is available, an evaluation of the system of equations allows todetermine different parameters of the mixture, as it is described in thefollowing. Preferably, the number of measurements is chosen to be sohigh that the system of equations is overdetermined and the parameterscan be determined by calculus of observations with high accuracy.

[0040] It is to be noted that besides equation (2) other approaches andapproximations exist that estimate the permittivity value ε_(m) of amixture. One other equation, described in DE 196 52 679, is the mixingformula of Polder-van Santen/de Loor. Furthermore, variousapproximations can e.g. be used for the depolarization factors. Forexample, by assuming rotational symmetry for the depolarization factorsof the free water, the following approximations can be used:

N₂₁=N₂₂=N_(fw)

N ₂₃=1−2·N _(fw),  (3)

[0041] i.e. the depolarization effects in the cavities of the free watercan be expressed by a single parameter N_(fw).

[0042] For the depolarization factors of gas, the following assumptionis found to be reasonable:

N ₁₁ =N ₁₂ =N ₁₃=1/3  (4)

[0043] For the depolarization factors of the bound water, the followingapproximation can be used:

N ₃₁ =N ₃₂=0 and N ₃₃=1.  (5)

[0044] In general, the mixing formula have, when the contribution ofbound water is taken into account, the following form

ε_(m)=ε_(m)(ε₁, ε₂, ε₃, ε_(b) , v ₁ , v ₂ , v ₃),  (6)

[0045] i.e. the permittivity value of the mixture is given as a functionof the permittivity values of the components and the volume fractions.Where applicable, further parameters can be taken into account asunknowns in equation (6), such as at least one depolarization factor ofa component of the mixture, in particular a depolarization factor offree water, e.g. the depolarization factor N_(fw) of equation (3).

[0046] If the contribution of the bound water is not taken into accountor neglected (or, taken into account in approximation as a constantcontribution to the permittivity value ε_(b) of the carrier substance),and if approximations of the type of equations (3), (4) and (5) are usedfor the depolarization factors, it results:

ε_(m)=ε_(m)(ε₁, ε₂, ε_(b) , v ₁ , v ₂ , N _(fw)).  (7)

[0047] Some of the parameters in equations (2), (6) or (7) can beestimated with sufficient accuracy, while others can only be determinedby the measurement.

[0048] The permittivity value ε₁ of the gas at the used frequencies canbe set to 1+0·i in good approximation.

[0049] For the permittivity value ε₂ of the free water the Cole-Coleapproximation can be used: $\begin{matrix}{{{ɛ_{2}(f)} = {ɛ_{\infty {({fw})}} + \frac{ɛ_{{stat}{({fw})}} - ɛ_{\infty {({fw})}}}{1 + \left( {i \cdot \omega \cdot \tau_{fw}} \right)^{1 - \alpha}} - {i \cdot \frac{\sigma_{fw}}{\omega \cdot ɛ_{o}}}}},} & (8)\end{matrix}$

[0050] with the parameters ε_(stat(fw)), ε_(∞(fw)), τ_(fw), α, andσ_(fw), wherein ε_(O)=8.8642×10⁻¹² F/m and ω=2πf. ε_(stat(fw))corresponds to the static dielectric constant of free water, ε_(∞(fw))to the dielectric constant of free water at optical frequencies, τ_(fw)to the relaxation time of free water, α=0.02 and σ_(fw) to theconductivity of free water. Numerical, temperature and salt dependentvalues of the corresponding parameters are published in ,,PermittivityMeasurements Using Open-Ended Sensors and Reference LiquidCalibration—An Uncertainty Analysis”, by A. Nyshadham et al., IEEETransactions on Microwave Theory and Techniques, Vol. 40(2), pp. 305ff,1992.

[0051] For the permittivity value ε₃ of the bound water, the Cole-Coleapproximation can be used as well: $\begin{matrix}{{{ɛ_{3}(f)} = {ɛ_{\infty {({bw})}} + \frac{ɛ_{{stat}{({bw})}} - ɛ_{\infty {({bw})}}}{1 + \left( {i \cdot \omega \cdot \tau_{bw}} \right)^{1 - \alpha}} - {i \cdot \frac{\sigma_{bw}}{\omega \cdot ɛ_{o}}}}},} & (9)\end{matrix}$

[0052] with the parameters ε_(stat(bw)), ε_(∞(bw)), τ_(bw), α, andσ_(bw) and with ε_(O)=8.8642×10⁻¹² F/m and ω=2πf. Preferably, thefollowing values are used:

[0053] ε_(stat(bw))≈80,

[0054] ε_(∞(bw))=4.5,

[0055] τ_(bw)≈7.721×10⁻¹⁴T³+1.017×10⁻¹¹T²31 5.516×10⁻¹⁰T+1.645×10⁻⁸seconds (temperature T in ° C.),

[0056] α=0, and

[0057] σ_(bw)°0.

[0058] The permittivity value ε_(b) of the carrier substance isgenerally known from calibration measurements.

[0059] The volume fractions v₁, v₂₃ and v₃ give, when added, theporosity of the carrier substance. If the contribution of the boundwater is not taken into account, v₃ can be set to zero. In manypractical applications, the volume fraction v₃ is a fixed quantity,because bound water is always present in the carrier substance and ishard to remove. For concrete, v₃ has a value of approximately 0.016.

[0060] From equation (7) (or equation (2) respectively, with v₃=0 andthe approximations (3) and (5)) a system of equations results when atleast four measuring values at different frequencies are evaluated andthe above values for the known parameters are used, which system ofequations allows the simultaneous determination of the following unknownparameters:

[0061] volume fraction v₁ of the gas,

[0062] volume fraction v₂ of the free water,

[0063] at lest one of the depolarization factors N_(2j) of the freewater, in particular N_(fw) when using the approximation (4), and

[0064] electric conductivity of the free water.

[0065] Instead of these parameters, other values depending on theseparameters can be determined. In particular, the salt contents of thefree water can e.g. be determined from the conductivity of the freewater by using empirical equations according to the above mentionedpublication of A. Nyshadham et al. Corresponding conversion formulas areknown to the person skilled in the art.

[0066] If the contribution of the bound water is not neglected and takenaccount of explicitly, the number of the unknown parameters increases.It is found, however, that it is still possible to make an accuratemeasurement when a good estimate for the permittivity value ε₃ is used.For this purpose it is important that it is taken into account that thispermittivity value ε₃ is frequency dependent at the used measuringfrequencies, i.e. in general ε₃=ε₃(f). For example, equation (9) can beused as specific formula. Depending on the frequency range, the realvalue of equation (9) can be set to a constant value of e.g. 4.5. Inparticular, as mentioned before, it can be said in good approximationthat, at the given frequency, the conductivity σ_(bw) of the bound wateris zero.

[0067] Hence, when taking the contributions of the free water intoaccount, at least one parameter, in particular the volume fraction v₂ ofthe free water, can be determined from equation (2) or (5) when enteringthe measuring values into the system of equations.

[0068] With the method described above, it is also possible to determinethe porosity of the carrier substance as a sum of the volume fractionsv₁+v₂ (or v₁+v₂+v₃ when taking the bound water into account).

[0069] Furthermore, the volumetric amount of water can be determinedwith the present method from the value v₂ or the sum v₂+v₃. When thepure density of the carrier substance is known and the known ordetermined porosity is taken into account, the weight fraction of watercontent can be determined as follows:

ρ_(roh)=ρ_(rein)·(1−θ)

with:

[0070] The pure density can be determined in simple manner in alaboratory by means of standard procedures.

[0071] In the above discussion it has been assumed that the permittivityvalue ε_(m) of the mixture is position independent. If this is not thecase, the measured value ε_(m) is an average value, i.e. an integralvalue, of the permittivity of the mixture within the measuring range 11of the sensor.

[0072] In particular for solid mixtures the permittivity value is,however, often a parametric function f of the depth, i.e. of thedistance from the surface, for example

f(x)=a1+a2(1−exp(−x/a3)),  (9)

[0073] wherein a1, a2 and a3 are unknown parameters.

[0074] It has been found that the present method allows thedetermination of the depth dependent liquid water fraction, or,analogously, of another depth dependent parameter (such as the saltcontent).

[0075] For this purpose, several measuring steps k are carried out,wherein in each measuring step the sensor is arranged at a knowndistance from the mixture and is separated from the same by a dielectricof known permittivity. The dielectric can, in particular, also be air,and in one of the measuring steps the distance is preferably 0. Betweenmeasuring steps, the distance between the sensor and the mixture ischanged, or another dielectric is introduced between the sensor and themixture. In most measuring steps, the measuring range of the sensor willtherefore enter only partially and in differently strong manner into themixture.

[0076] In each measuring step, a value w_(k) depending on the integralpermittivity value ε_(mk) is measured, such as e.g. the water fractionor the salt content. For this purpose, it can e.g. be assumed that thepermittivity value ε_(m) is constant over the measuring range, such thatthe above evaluations can be used. From the changing dependence of thevalues w_(k) from the parameter to be measured (such as the waterfraction) in the measuring range, the values a1, a2, a3 and thereforethe function f can be determined.

[0077] Preferably, the integral

w _(k) =∫E _(k)(x)f _(a1,a2, . . .) (x)dx  (10)

[0078] is calculated for each measuring step k, wherein E_(k)(x) is anormalized dependence of the sensitivity of the sensor from the depth xin the mixture in the conditions of measuring step k (distance betweensensor and mixture and permittivity of the dielectric).

[0079] The dependence E_(k)(x) can e.g. be determined by previouscalibration measurements under the measuring conditions of the measuringstep, or numerically, e.g. by finite element calculus.

[0080] For example, it can be based on the sensitivity S(x) of thesensor lying against the mixture. If the distance between sensor andmixture in measuring step k is equal to d_(k) and the permittivity valueof the dielectric between sensor and mixture is approximately equal tothe average permittivity value of the mixture, we get in approximation:

E _(k)(x)=S(x+d _(k))  (11)

[0081] By entering the measuring values w_(k) in equation (10), it isagain possible to set up a system of equations for the parameters a1,a2, a3 . . . , which can be solved by means of the calculus ofobservations.

[0082] While, in the present application, preferred embodiments of theinvention are described, it is to be distinctly understood that theinvention is not limited thereto and can also be carried out indifferent manner within the scope of the following claims.

1. A method for determining at least one parameter of a mixture of thecomponents of a carrier substance, water and gas, comprising thefollowing steps: bringing the mixture into a measuring range of asensor, measuring complex permittivity values ε_(m)(f_(i)) of themixture at several measuring frequencies f_(i) by feeding anelectromagnetic wave to the sensor and by means of calibration data ofthe sensor, establishing a system of equations by entering thepermittivity values ε_(m)(f_(i)) into a mixing formula ε_(m)=ε_(m)(ε₁,ε₂, ε₃, ε_(b) , v ₁ , v ₂ , v ₃),  returning the permittivity valueε_(m)(f) of the mixture at least as a function of the permittivityvalues and the volume fractions ε₁ and v₁ of the gas, ε₂ and v₂ of freewater and ε₃ and v₃ of bound water and as a function of the permittivityvalue ε_(b) of the carrier substance, and determining at least oneunknown parameter of the mixing formula or a parameter derived from theunknown parameter by evaluating the system of equations, characterizedin that the permittivity value ε₃ of the bound water is inserted as afrequency dependent function ε₃(f) into the mixing formula.
 2. Themethod of claim 1 wherein the mixing formula depends on at least onedepolarization factor, in particular of a depolarization factor of freewater.
 3. A method for determining parameters of a mixture of thecomponents of a carrier substance, free water and gas, comprising thefollowing steps: bringing the mixture into a measuring range of asensor, measuring complex permittivity values ε_(m)(f_(i)) of themixture at several measuring frequencies f_(i) by feeding anelectromagnetic wave to the sensor and by means of calibration data ofthe sensor, establishing a system of equations by entering thepermittivity values ε_(m)(f_(i)) into a mixing formula ε_(m)=ε_(m)(ε₁,ε₂, ε_(b) , v ₁ , v ₂ , N _(fw)),  returning the permittivity valueε_(m)(f) of the mixture as a function of the permittivity values and thevolume fractions ε₁ and v₁ of the gas, ε₂ and v₂ of the free water andas a function of the permittivity value ε_(b) of the carrier substanceand a depolarization coefficient N_(fw) of the free water and neglectinga contribution of bound water, and determining the following parameters,or values depending on the following parameters, from the system ofequations: volume fraction v₁ of the gas, volume fraction v₂ of the freewater, the depolarization factors N_(fw) of the free water andconductivity of the free water.
 4. A method, in particular of any of thepreceding claims, for determining at least one parameter of a mixture ofthe components of a carrier substance, water and gas, comprising thefollowing steps: bringing the mixture into a measuring range of asensor, measuring complex permittivity values ε_(m)(f_(i)) of themixture at several measuring frequencies f_(i) by feeding anelectromagnetic wave to the sensor and by means of calibration data ofthe sensor, establishing a system of equations by entering thepermittivity values ε_(m)(f_(i)) into a mixing formula$ɛ_{m} = {ɛ_{b} + {\sum\limits_{i = 1}^{n}\quad {\frac{v_{i}}{3} \cdot \left( {ɛ_{i} - ɛ_{b}} \right) \cdot {\sum\limits_{j = 1}^{3}\quad \frac{ɛ_{m}}{ɛ_{m} + {N_{ij} \cdot \left( {ɛ_{i} - ɛ_{m}} \right)}}}}}}$

 with ε₁ and v₁ being the permittivity value and the volume fraction ofthe gas, ε₂ and v₂ the permittivity value and the volume fraction of thefree water, ε₃ and v₃ the permittivity value and the volume fraction ofthe bound water, ε_(b) the permittivity value of the carrier substance,and N_(1j), N_(2j) and N_(3j) the depolarization factors of anellipsoidal cavity of the gas or the free water or the bound water,respectively, wherein n=3 when taking the bound water into account andn=2 when neglecting the bound water, and determining at least oneunknown parameter of the mixing formula, or of a value derived from theunknown parameter, by evaluating the system of equations.
 5. The methodof claim 4 wherein one of the depolarization factors N_(2j) of the freewater is determined from the system of equations, and in particular thatN₂₁=N₂₂=N_(fw)=N₂₃=1−2·N_(fw) is used and the value of N_(fw) isdetermined from the system of equations.
 6. The method of any of theclaims 4 to 5 wherein for bound water N₂₁=N₃₂=0 and N₃₃=1 is used. 7.The method of any of the claims 4 to 6 wherein for the gasN₁₁=N₁₂=N₁₃=1/3 is used.
 8. The method of any of the preceding claimscharacterized in that for the permittivity value of the bound water thefollowing frequency dependent function ε₃(f) is inserted into the mixingformula:${{ɛ_{3}(f)} = {ɛ_{\infty {({bw})}} + \frac{ɛ_{{stat}{({bw})}} - ɛ_{\infty {({bw})}}}{1 + \left( {i \cdot \omega \cdot \tau_{bw}} \right)^{1 - \alpha}} - {i \cdot \frac{\sigma_{bw}}{\omega \cdot ɛ_{o}}}}},$

with the parameters ε_(stat(bw)), ε_(∞(bw)), τ_(bw), α, and σ_(bw) andwith ε_(O)=8.8642×10¹² F/m and ω=2πf, and in particular thatε_(stat(bw)) is approximately equal to 80 and/or ε_(∞(bw)) isapproximately equal to 4.5 and/or τ_(bw) is, depending on a measuredtemperature T in degree Celsius, approximately equal to−7.721×10⁻¹⁴T³+1.017×10⁻¹¹T²−5.516×10⁻¹⁰T+1.645×10⁻⁸ seconds, and/or αis set to zero and/or σ_(bw) is set to zero.
 9. The method of any of thepreceding claims wherein the volume fraction v₃ of the bound water isinserted as a constant quantity into the system of equations and inparticular that v₃ is set approximately equal to 0.016 for concrete. 10.The method of any of the preceding claims characterized in that thefollowing frequency dependent function ε₂(f) is inserted into the mixingformula for the permittivity value of the free water:${{ɛ_{2}(f)} = {ɛ_{\infty {({fw})}} + \frac{ɛ_{{stat}{({fw})}} - ɛ_{\infty {({fw})}}}{1 + \left( {i \cdot \omega \cdot \tau_{fw}} \right)^{1 - \alpha}} - {i \cdot \frac{\sigma_{fw}}{\omega \cdot ɛ_{o}}}}},$

with the parameters ε_(stat(fw)), ε_(∞(fw)), τ_(fw), α, and σ_(fw) andwith ε_(O)=8.8642×10⁻¹² F/m and ω=2πf, wherein ε_(stat(fw)) correspondsto the static dielectric constant of free water, ε_(∞(fw)) to thedielectric constant of free water at optical frequencies, τ_(fw) to arelaxation time of free water and σ_(fw) to a conductivity of freewater.
 11. The method of claim 10 wherein the conductivity σ_(fw) offree water is determined.
 12. The method of any of the preceding claimswherein using the system of equations a salt concentration in the freewater is determined from a dependence of the imaginary part of thepermittivity of the free water from the conductivity σ_(fw) of the freewater.
 13. The method of any of the preceding claims wherein the carriersubstance is a solid with pores and wherein the gas and the water are inthe pores.
 14. The method of claim 13 wherein the carrier substance isconcrete.
 15. The method of any of the preceding claims wherein thetemperature of the mixture is measured.
 16. The method of any of thepreceding claims wherein the sensor is placed as a surface sensor onto asmooth, flat surface of the carrier substance or the carrier substanceis filled into the sensor in liquid form.
 17. The method of any of thepreceding claims wherein measurements are made at at least threedifferent frequencies.
 18. The method of any of the preceding claimswherein a porosity of the carrier substance is determined from the sumof the volume fractions.
 19. The method of any of the preceding claimscharacterized in that the measuring frequencies are in a range of 10 kHzand 10 GHz, in particular of 10 MHz to 1 GHz.
 20. The method of any ofthe preceding claims wherein the volume fraction v₂ of the free water isdetermined from the system of equations.
 21. A method for determining adepth dependent parameter, in particular the amount of water, of amixture with the components of a carrier substance, water and gas, inparticular of any of the preceding claims, comprising several measuringsteps k, wherein at least in a part of the measuring steps a sensor isarranged at a known distance from the mixture and is separated from thesame by a dielectric of known permittivity, such that a measuring rangeof the sensor is extending to different depths in the differentmeasuring steps, wherein, by means of the sensor, a value w_(k)depending on an integral permittivity value ε_(mk) of the mixture in themeasuring range is measured, and an evaluation in which a depthdependence of the liquid water fraction is determined based on adependency of the values w_(k) from the parameter to be determined. 22.The method of claim 21 wherein in the evaluation a parametric functionof the parameter is fitted to the values w_(k).
 23. The method of any ofthe claims 21 or 22 wherein, between the measuring steps, the distancebetween the sensor and the mixture is changed and/or differentdielectrics are arranged between the sensor and the mixture.
 24. Themethod of any of the claims 21 to 23 wherein the effective permittivityvalue is determined under the assumption that the parameter to bemeasured is constant over the measuring range.
 25. The method of any ofthe claims 21 to 24, wherein for each measuring step k the integral w_(k) =∫E _(k)(x)f _(a1,a2, . . .) (x)dx, is calculated, wherein E_(k)(x)is a normalized dependence of a sensitivity of the sensor from the depthx in the mixture at a given distance between the sensor and the mixtureand permittivity of the dielectric in the measuring step k, andf_(a1,a2,a3, . . .) (x) is a depth dependent distribution of theparameter in the mixture with parameters a1, a2, a3 . . . , wherein theparameters a1, a2, a3 . . . are determined from the integrals of themeasuring steps by means of calculus of observations.
 26. A device forcarrying out the method of any of the preceding claims, characterized inthat it comprises a sensor (2, 3), a measuring apparatus (1) for afrequency dependent measurement of the sensor, and a data processingapparatus (4), wherein the data processing apparatus (4) is designed fordetermining the parameter to be determined according to any of thepreceding claims.
 27. The device of claim 26 wherein the sensor (2) is asurface sensor (2) or a waveguide sensor (3).
 28. The device of any ofthe claims 26 or 27, wherein a coaxial transmission line (14) isarranged between the sensor (2, 3) and the measuring apparatus (1) andthe sensor (2, 3) comprises a tapered transition section (12) for animpedance matched connection to the coaxial transmission line (14). 29.The device of any of the claims 26 to 28 wherein the measuring apparatus(1) comprises a vector network analyzer, and a reflection and/ortransmission factor determined by the network analyzer can be convertedinto a permittivity of the mixture by means of sensor specificcalibration data.